MathDB

22

Part of 2017 Harvard-MIT Mathematics Tournament

Problems(1)

2017 Guts #22: Fighting frogs

Source:

2/21/2017
Kelvin the Frog and 1010 of his relatives are at a party. Every pair of frogs is either friendly or unfriendly. When 33 pairwise friendly frogs meet up, they will gossip about one another and end up in a fight (but stay friendly anyway). When 33 pairwise unfriendly frogs meet up, they will also end up in a fight. In all other cases, common ground is found and there is no fight. If all (113)\binom{11}{3} triples of frogs meet up exactly once, what is the minimum possible number of fights?
combinatorics